Conceptual Physics
Notes on Chapter 15-18
Temperature, Heat, Heat
Transfer, change of phase,
and thermodynamics
Temperature
•
All matter—solid, liquid, and
gas—is composed of
continuously jiggling atoms or
• When a solid, liquid, or gas gets
warmer, its atoms or molecules
molecules.
•
move faster
Because of this random motion,
the atoms and molecules in
• The increased movement
causes an increase in heat
matter have kinetic energy
•
Thermometer
•
The first “thermal meter” for was
•
quantity of matter by a number that
invented by Galileo in 1602
corresponds to its degree of hotness
• The familiar mercury-in-glass
thermometer came into
widespread use some seventy
years later.
• Mercury thermometers are being
phased out because of the danger
of mercury poisoning
We express the temperature of some
or coldness on some chosen scale.
•
Nearly all materials expand when
their temperature is raised and
contract when their temperature is
lowered. Most thermometers
measure temperature by means of
the expansion or contraction of a
liquid, usually mercury or colored
alcohol, in a glass tube with a scale.
http://www.solarcooking.org/pla
ns/
American Solar Challenge
http://americansolarchallenge.org/ev
ents/asc2010/
Temperature, Heat, Heat Transfer
• This is going to be a REVIEW of last years
chemistry class.
• However, we are going to look at this from a
PHYSICS perspective.
Temperature, Heat, Heat Transfer
• All matter is composed of “jiggling” atoms.
This matter has kinetic energy (Ch.8).
• This kinetic energy causes an effect we call
warmth or TEMPERATURE.
• Cold objects have Less kinetic energy.
• Hot objects have More kinetic energy.
Temperature, Heat, Heat Transfer
• Most objects expand when it gains energy and
contracts when it losses energy. A
Thermometer is a good example.
• Celsius Scale
• Fahrenheit Scale
• Kelvin Scale
•
•
•
Celsius Scale – named in honor of astronomer Andres Celsius (1701 – 1744).
Fahrenheit Scale - named in honor of German physicist Gabriel Fahrenheit (1686 – 1736).
Kelvin Scale - named in honor of British physicist Lord Kelvin (1824 – 1907).
Temperature, Heat, Heat Transfer
• The energy that transfers from one object to another because
of a temperature difference between them is called HEAT.
– Note: Matter DOES NOT contain heat.
• Matter contains ENERGY in the form of heat.
• The grand total of all energies inside a substance is called
INTERNAL ENERGY.
– A substance that does not contain heat, still contains internal energy
(atoms vibrating).
Temperature, Heat, Heat Transfer
Measurement of Heat
• The most common unit of heat is
the CALORIE. The calorie is
defined as the amount of heat
required to raise the temperature
of 1 gram of water by 1°C.
• IMPORTANT: Calorie and calorie
are both units of energy. Calorie is
the Food version.
Temperature, Heat, Heat Transfer
Specific Heat Capacity
• Different objects have different
capacities for storing internal
energy.
– Aluminum foil cools very
rapidly…food in container does
not!
• We call this
Specific heat capacity.
Temperature, Heat, Heat Transfer
Applications
• This leads to increased “jiggle” of atoms which tend to
move apart. The result is EXPANSION of the substance.
– Bimetallic strip … Thermostat
– Bridge Gaps
– Jar lids
Temperature, Heat, Heat Transfer
Conduction, Convection, Radiation
• Conduction
– The direct transfer or movement of warmth and energy from one molecule to
another molecule by collision.
• Convection
– The organized motion or movement of large groups of molecules based on
their relative densities or temperatures.
• Radiation
– The method by which the sun's energy reaches the earth
Temperature, Heat, Heat Transfer
Newton’s Law of Cooling
• Newton's Law of Cooling states that the rate of
change of the temperature of an object is
proportional to the difference between its own
temperature and the ambient temperature (i.e. the
temperature of its surroundings).
Temperature, Heat, Heat Transfer
Global Warming & the
Greenhouse Effect
• Earth’s atmosphere is
transparent to solar
energy. This traps the
energy…the greenhouse
effect.
Temperature, Heat, Heat Transfer
Global Warming & the
Greenhouse Effect
• This is good in that it
helps heat the earth.
– HOWEVER…to much
heating leads to global
warming.
Chapter 16: Temperature and Heat
Temperature is a fundamental quantity which
characterizes the physical state of a substance. In
the microscopic statistical theory, we understand
temperature as the average energy per degree of
freedom of motion of the substance.
Heat is an interaction between two objects,
particularly the flow of energy from one object to
another.
When two objects are placed in thermal contact (so
that heat is able to flow from one to the other), heat
will flow until the temperatures of the two objects
are the same. Then the two objects are in thermal
equilibrium.
Temperature Scales
Celsius – water freezes at 0 °C and
boils at 100 °C
Fahrenheit – water freezes at 32 °F
and boils at 212 °F
Kelvin - water freezes at 273.15 K and
boils at 373.15 K.
But how do we determine the equal
divisions between these
calibration points?
Absolute Zero – the lowest possible
temperature: 0 K = –273.15 °C
TK = TC + 273.15
Thermal Expansion
Most substances expand when heated. They expand in
all dimensions
Conceptual Checkpoint 16-3: A washer has a hole in the
middle. As the washer is heated does the hole (a)
expand, (b) shrink, or (c) stay the same?
Hint, what happens to the
piece cut out to make the
hole?
Water is special!
Water is an
exception to the
rule. Between 0
and 4 °C it
contracts. Above
4 °C it expands.
Water is most
dense at 4 °C.
Precurser to fact that ice
floats!
(most solids sink in their
own liquid)
Thermal Expansion.
Thermometers & Thermostats
•
•
Use the expansion of Hg to define a
temperature scale.
Use the differential expansion of two
dissimilar metals to make either a
thermometer or a thermostat
(temperature activated switch)
Thermal Expansion Coefficient
• Any linear dimension L of a solid object with
expand (or contract) with temperature changes.
• If L is the length at temperature T0, then
• L(T0 +DT) = L + DL
• DL = a L DT
• (DL/L) = a DT
• a is the coefficient of linear expansion
 a itself can be a function of temperature
 a(water) < 0 for 0º C < T < 4º C
 a(Cu) = 17·10-6 / (º C)
 1degree Celsius change causes a fractional expansion of 17
parts per million.
Thermometers & Thermostats
•
•
Use the expansion of Hg to define a
temperature scale.
Use the differential expansion of two
dissimilar metals to make either a
thermometer or a thermostat
(temperature activated switch)
s0 = unheated common length
R = radius of curvature of heated metal A
s = Rq = heated length of metal A
R+dr = radius of curvature of heated metal B
s+ds = (R+dr)q = length of heated metal B
ds = q dr = s0(1+aBDT) - s0(1+aADT)
ds = s0 ( aB - aA )DT
ds = differential thermal expansion of metals A& B.
Absolute Zero
• Ideal Gas Law (Chapter 17)
• Constant Volume GasThermometer.
 Keep the reference level fixed =
fixed gas volume.
 Adjust height as temperature of
gas is varied
 Pressure of gas = r g h
 Pressure curves extrapolate
to a common zero pressure at
a common temperature
 T = -273.15 C = -460F
http://jersey.uoregon.edu/vlab/Piston/
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/gaslaws3.h
tml

an 2 
P 
 V - nb   nRT
2

V 
Compound a( L2atm / mol 2 ) b( L / mol )
He
0.034
0.0237
Ne
0.211
0.017
H2
0.2444
0.02661
O2
1.345
0.03219
CO2
3.592
0.04267
H2 & N2 at 0deg C
CO2 at 40deg C
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/deviation5.ht
Heat
Heat Q is the energy transferred between one
object and another due to temperature
differences. Heat is measured in calories (cal).
1 cal = 4.186 J
A Calorie (C) is a kilocalorie.
Salad oil: 8.6kC / kg  8.6 kC /litre=36·106 J/litre
Gasoline has only slightly greater energy density
Mechanical energy can be converted into heat.
Examples?
Solar Energy & Agriculture
• The solar flux is 1 kW/m2.
– The atmosphere absorbs about ½, we lose ½ for night time, the
growing season is ½ the year, ½ the days are cloudy.
– Modern agriculture is about 3% efficient at turning solar energy
into plant chemical energy. Assume ¼ of this can be recovered in
a seed oil (sunflower, etc), convertible to diesel.
• Total yield of 1 hectare: 100m x 100 m
– (1000 W/m2) (104 m2) (1/2)4 (0.03) (1/4)  1 Cal/s
• Gasoline consumption 1 gallon/person/day
– 1 gallon oil/day  34,000 Cal/day = 0.4 Cal/s
• We could power all of our vehicles on bio-diesel,
– But modern agriculture uses 1 gallon of fossil fuel to make 1
gallon of bio-diesel.
– Need a non-fossil fuel dependent agriculture.
Specific Heat
If you add heat to a substance its temperature will
increase. But how much? That depends on the
specific heat of the substance.
Q = mcDT
Q = heat added
m= mass
c = specific heat
DT = change in temperature
Water has a very large heat capacity; a lot of energy transfer
(heat) is required to change its temperature. This has a
major impact on the climate.
Water: c = 1.0 cal /(ºC g) = 1.0 Cal /(ºC kg)
It takes one calorie to raise the temperature of 1 gm of water
by 1 degree Celsius (use this to define 1 calorie).
Mechanical Equivalent of Heat
• Conservation of energy can be broadened to
include thermal energy
• Work done on system by non-conservative
forces = heat = thermal energy added to
system
 Rub your hands to warm them (work done by
friction).
 1 calorie = 4.18 Joule
Specific Heat, values
• Table 16-2
Substance
Specific Heat
[J / (kg K)]
Specific Heat
[cal/(kg K)]
Water
4186
1000
Ice
2090
500
Air
1004
240
Gold
129
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Walker Problem 29, pg 530
1.0-g lead pellets at 75 °C are to be added to 180 g
of water at 22 °C. How many pellets are needed to
increase the equilibrium temperature to 25 °C?
Conduction
There are three ways in which heat can be transferred
from one object to another:
•Conduction – when two objects are in physical
contact.
 DT 
Q  kA
t
 L 
k = thermal conductivity
Q = heat transferred
A = cross sectional area
t = duration of heat transfer
L = length
DT = temperature difference between
two ends
In a hot oven the air and the
metal rack are at the same
temperature, but which one
feels hotter and why?
Thermal Conductivities,
Table 16-3
• Metals have high
thermal
conductivity, most
electrical insulators
also have low
thermal
conductivity.
• Air is a great
insulator, except
that large air spaces
allow heat flow by
convection.
Substance
Thermal
Conductivity: k
W / (m K)
Gold
291
Glass
0.84
Water
0.60
Wood
0.10
Air
0.023
Convection and Radiation
• Convection – when heat is carried by a moving fluid
Heat house with radiator
Gulf stream transports Heat from Caribbean to Europe
Cold air inside window (in winter) sinks, creates convection = cold draft
• Radiation – when electromagnetic waves (radiation)
carry heat from one object to another.
Example: heat you feel when you are near a fire
Example: Heat from the sun
Formation of frost (ice) at night,
T(air) > 0ºC, but surface temp drops below 0ºC.
Black Body Radiation
• Any object heated to a temperature T (on an absolute scale)
radiates Electromagnetic Energy (light) with total power:
P = e s A T4





0<e<1 = emissivity = property of material
s = 5.67 ·10 –8 W/(m2 K4)
A = surface area of object
Peak wavelength occurs at l = (5.1·10-3 m ·K ) / T
(Chap 30)
Early triumph of quantum theory (M. Planck) to predict Power and
wavelength equations, including the values of the constants, with just
one free parameter (now called Planck’s constant).
• If the surroundings have temperature TS, then the net power
radiated is
• P = e s A [ T4 - TS4]
• Dark, dry, night, TS = 3 K, Black body radiation cools the
surface faster than conduction can transport heat from the
ground or air. Frost can form even if air temperature > 0C.
Linear Dimension & Area
A disk has radius r. Which is true:
1.
2.
The circumference of the disk is 2pr and
the area is pr2
The circumference of the disk is pr2 and
the area is 2pr
Thermal Expansion
A metal disk of radius r = 5.00 cm and thickness
d=1.00mm is heated such that every linear dimension
expands to 1.001 times its original length.

What is the fractional change fC=(2pr’)/(2pr) in the
circumference of the disk?
1. 0.999
2. 1.000001
3. 1.001
4. 1.0020011.002
Thermal Expansion
A metal disk of radius r = 5.00 cm and thickness
d=1.00mm is heated such that every linear dimension
expands to 1.001 times its original length.

What is the fractional change fA=(pr’2)/(pr2) in the area of the disk?
1. 0.999
2. 1.000001
3. 1.001
4. 1.0020011.002
Heat Engines, Heat Pumps, and
Refrigerators
Getting something useful from heat
Heat can be useful
• Normally heat is the end-product of the
flow/transformation of energy
– remember examples from lecture #4 (coffee mug,
automobile, bouncing ball)
– heat regarded as waste: as useless end result
• Sometimes heat is what we want, though
– hot water, cooking, space heating
• Heat can also be coerced into performing
“useful” (e.g., mechanical) work
– this is called a “heat engine”
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Heat Engine Concept
• Any time a temperature difference exists between
two bodies, there is a potential for heat flow
• Examples:
– heat flows out of a hot pot of soup
– heat flows into a cold drink
– heat flows from the hot sand into your feet
• Rate of heat flow depends on nature of contact
and thermal conductivity of materials
• If we’re clever, we can channel some of this flow
of energy into mechanical work
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Heat  Work
• We can see examples of heat energy producing
other types of energy
–
–
–
–
–
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Air over a hot car roof is lofted, gaining kinetic energy
That same air also gains gravitational potential energy
All of our wind is driven by temperature differences
We already know about radiative heat energy transfer
Our electricity generation thrives on temperature
differences: no steam would circulate if everything
was at the same temperature
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Power Plant Arrangement
Heat flows from Th to Tc, turning turbine along the way
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Heat Engine Nomenclature
• The symbols we use to describe the heat engine are:
–
–
–
–
–
–
–
–
–
–
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Th is the temperature of the hot object (typ. in Kelvin)
Tc is the temperature of the cold object (typ. in Kelvin)
DT = Th–Tc is the temperature difference
DQh is the amount of heat that flows out of the hot body
DQc is the amount of heat flowing into the cold body
DW is the amount of “useful” mechanical work
DSh is the change in entropy of the hot body
DSc is the change in entropy of the cold body
DStot is the total change in entropy (entire system)
DE is the entire amount of energy involved in the flow
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What’s this Entropy business?
• Entropy is a measure of disorder (and actually
quantifiable on an atom-by-atom basis)
– Ice has low entropy, liquid water has more, steam
has a lot
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The Laws of Thermodynamics
1. Energy is conserved
2. Total system entropy can never decrease
3. As the temperature goes to zero, the entropy
approaches a constant value—this value is zero
for a perfect crystal lattice
• The concept of the “total system” is very
important: entropy can decrease locally, but it
must increase elsewhere by at least as much
– no energy flows into or out of the “total system”: if it
does, there’s more to the system than you thought
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Q
Quantifying heat energy
• We’ve already seen many examples of quantifying heat
– 1 Calorie is the heat energy associated with raising 1 kg (1 liter) of
water 1 ºC
– In general, DQ = cpmDT, where cp is the heat capacity
• We need to also point out that a change in heat energy
accompanies a change in entropy:
DQ = TDS
(T expressed in K)
• Adding heat increases entropy
– more energy goes into random motionsmore randomness (entropy)
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How much work can be extracted from
heat?
Hot source of energy
Th
DQh heat energy delivered from source
externally delivered work:
DW = DQh – DQc
heat energy delivered to sink DQc
conservation of energy
efficiency =
Cold sink of energy
Tc
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DW work done
=
DQh heat supplied
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Q
Let’s crank up the efficiency
Let’s extract a lot of
work, and deliver very
little heat to the sink
Th
DQh
DW = DQh – DQc
In fact, let’s demand 100%
efficiency by sending no heat
to the sink: all converted
to useful work
DQc
efficiency =
Tc
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DW work done
=
DQh heat supplied
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Not so fast…
• The second law of thermodynamics imposes a
constraint on this reckless attitude: total entropy
must never decrease
• The entropy of the source goes down (heat
extracted), and the entropy of the sink goes up
(heat added): remember that DQ = TDS
– The gain in entropy in the sink must at least balance
the loss of entropy in the source
DStot = DSh + DSc = –DQh/Th + DQc/Tc ≥ 0
DQc ≥ (Tc/Th)DQh sets a minimum on DQc
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What does this entropy limit mean?
• DW = DQh – DQc, so DW can only be as big as the minimum
DQc will allow
DWmax = DQh – DQc,min = DQh – DQh(Tc/Th) = DQh(1 – Tc/Th)
• So the maximum efficiency is:
maximum efficiency = DWmax/DQh = (1 – Tc/Th) = (Th – Tc)/Th
this and similar formulas must have the temperature in Kelvin
• So perfect efficiency is only possible if Tc is zero (in ºK)
– In general, this is not true
• As Tc  Th, the efficiency drops to zero: no work can be
extracted
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Examples of Maximum Efficiency
• A coal fire burning at 825 K delivers heat energy
to a reservoir at 300 K
– max efficiency is (825 – 300)/825 = 525/825 = 64%
– this power station can not possibly achieve a higher
efficiency based on these temperatures
• A car engine running at 400 K delivers heat
energy to the ambient 290 K air
– max efficiency is (400 – 290)/400 = 110/400 = 27.5%
– not too far from reality
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Q
Example efficiencies of power plants
Power plants these days (almost all of which are heat-engines)
typically get no better than 33% overall efficiency
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What to do with the waste heat
(DQc)?
• One option: use it for space-heating locally
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Overall efficiency greatly enhanced by
cogeneration
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Heat Pumps
Heat Pumps provide a means to very efficiently move heat
around, and work both in the winter and the summer
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Heat Pump Diagram
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Heat Pumps and Refrigerators:
Thermodynamics
Just a heat engine run
Hot entity
(indoor air)
Th
backwards…
heat energy delivered DQh
delivered work:
DW = DQh – DQc
conservation of energy
heat energy extracted DQc
efficiency =
Cold entity
(outside air or refrigerator)
Tc
(heat pump)
efficiency =
(refrigerator)
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DQh heat delivered
DW= work done
DQc heat extracted
DW= work done
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Heat Pump/Refrigerator Efficiencies
• Can work through same sort of logic as before to
see that:
– heat pump efficiency is: Th/(Th – Tc) = Th/DT
– refrigerator efficiency is: Tc/(Th – Tc) = Tc/DT
in ºK
in ºK
• Note that heat pumps and refrigerators are most
efficient for small temperature differences
– hard on heat pumps in very cold climates
– hard on refrigerators in hot settings
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Example Efficiencies
• A heat pump maintaining 20 ºC when it is –5 ºC
outside has a maximum possible efficiency of:
293/25 = 11.72
– note that this means you can get almost 12 times the
heat energy than you are supplying in the form of
work!
– this factor is called the C.O.P. (coefficient of
performance)
• A freezer maintaining –5 ºC in a 20 ºC room has a
maximum possible efficiency of:
268/25 = 10.72
– called EER (energy efficiency ratio)
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Example Labels (U.S. & Canada)
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Announcements and Assignments
• Chapter 3 goes with this lecture
• HW #3 due Thursday 4/23:
– primarily Chapter 2-related problems: (show work
or justify answers!); plus Additional problems (on
website)
• Remember that Quizzes happen every week
– available from Thurs. 1:50 PM until Friday 7:00 PM
– three attempts (numbers change)
• the better to learn you with
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